Mircea Galiceanu

Spectra of Husimi cacti: Exact results and applications

Starting from exact relations for finite Husimi cacti we determine their complete spectra to very high accuracy. The Husimi cacti are dual structures to the dendrimers but, distinct from these, contain loops. Our solution makes use of a judicious analysis of the normal modes. Although close to those of dendrimers, the spectra of Husimi cacti differ. From the wealth of applications for measurable quantities which depend only on the spectra, we display for Husimi cacti the behavior of the fluorescence depolarization under quasiresonant Forster energy transfer.

Dynamics of semiflexible scale-free polymer networks

Scale-free networks are structures, whose nodes have degree distributions that follow a power law. Here we focus on the dynamics of semiflexible scale-free polymer networks. The semiflexibility is modeled in the framework of [M. Dolgushev and A. Blumen, J. Chem. Phys. 131, 044905 (2009)], which allows for tree-like networks with arbitrary architectures to include local constrains on bond orientations. From the wealth of dynamical quantities we choose the mechanical relaxation moduli (the loss modulus) and the static behavior is studied by looking at the radius of gyration. First we study the influence of the network size and of the stiffness parameter on the dynamical quantities, keeping constant γ, a parameter that measures the connectivity of the scale-free network. Then we vary the parameter γ and we keep constant the size of the structures. This fact allows us to study in detail the crossover behavior from a simple linear semiflexible chain to a star-like structure. We show that the semiflexibility of the scale-free networks clearly manifests itself by displaying macroscopically distinguishable behaviors.

Relaxation dynamics of multilayer triangular Husimi cacti

We focus on the relaxation dynamics of multilayer polymer structures having, as underlying topology, the Husimi cactus. The relaxation dynamics of the multilayer structures is investigated in the framework of generalized Gaussian structures model using both Rouse and Zimm approaches. In the Rouse type-approach, we determine analytically the complete eigenvalues spectrum and based on it we calculate the mechanical relaxation moduli (storage and loss modulus) and the average monomer displacement. First, we monitor these physical quantities for structures with a fixed generation number and we increase the number of layers, such that the linear topology will smoothly come into play. Second, we keep constant the size of the structures, varying simultaneously two parameters: the generation number of the main layer, G, and the number of layers, c. This fact allows us to study in detail the crossover from a pure Husimi cactus behavior to a predominately linear chain behavior. The most interesting situation is found when the two limiting topologies cancel each other. For this case, we encounter in the intermediate frequency/time domain regions of constant slope for different values of the parameter set (G, c) and we show that the number of layers follows an exponential-law of G. In the Zimm-type approach, which includes the hydrodynamic interactions, the quantities that describe the mechanical relaxation dynamics do not show scaling behavior as in the Rouse model, except the limiting case, namely, a very high number of layers and low generation number.

Complex quantum networks: From universal breakdown to optimal transport.

We study the transport efficiency of excitations on complex quantum networks with loops. For this we consider sequentially growing networks with different topologies of the sequential subgraphs. This can lead either to a universal complete breakdown of transport for complete-graph-like sequential subgraphs or to optimal transport for ringlike sequential subgraphs. The transition to optimal transport can be triggered by systematically reducing the number of loops of complete-graph-like sequential subgraphs in a small-world procedure. These effects are explained on the basis of the spectral properties of the networks Hamiltonian. Our theoretical considerations are supported by numerical Monte Carlo simulations for complex quantum networks with a scale-free size distribution of sequential subgraphs and a small-world-type transition to optimal transport.

The rubber band revisited: Wang?Landau simulation

In this work we apply Wang–Landau simulations to a simple model which has exact solutions both in the microcanonical and canonical formalisms. The simulations were carried out by using an updated version of the Wang–Landau sampling. We consider a homopolymer chain consisting of N monomers units which may assume any configuration on the two-dimensional lattice. By imposing constraints to the moves of the polymers we obtain three different models. Our results show that updating the density of states only after every N monomer moves leads to a better precision. We obtain the specific heat and the end-to-end distance per monomer and test the precision of our simulations by comparing the location of the maximum of the specific heat with the exact results and conventional Wang–Landau simulations for the three types of walk.

Relaxation dynamics of Sierpinski hexagon fractal polymer: Exact analytical results in the Rouse-type approachand numerical results in the Zimm-type approach

In this paper, we focus on the relaxation dynamics of Sierpinski hexagon fractal polymer. The relaxation dynamics of this fractal polymer is investigated in the framework of the generalized Gaussian structure model using both Rouse and Zimm approaches. In the Rouse-type approach, by performing real-space renormalization transformations, we determine analytically the complete eigenvalue spectrum of the connectivity matrix. Based on the eigenvalues obtained through iterative algebraic relations we calculate the averaged monomer displacement and the mechanical relaxation moduli (storage modulus and loss modulus). The evaluation of the dynamical properties in the Rouse-type approach reveals that they obey scaling in the intermediate time/frequency domain. In the Zimm-type approach, which includes the hydrodynamic interactions, the relaxation quantities do not show scaling. The theoretical findings with respect to scaling in the intermediate domain of the relaxation quantities are well supported by experimental results.

Continuous-time quantum walks on multilayer dendrimer networks

We consider continuous-time quantum walks (CTQWs) on multilayer dendrimer networks (MDs) and their application to quantum transport. A detailed study of properties of CTQWs is presented and transport efficiency is determined in terms of the exact and average return probabilities. The latter depends only on the eigenvalues of the connectivity matrix, which even for very large structures allows a complete analytical solution for this particular choice of network. In the case of MDs we observe an interplay between strong localization effects, due to the dendrimer topology, and good efficiency from the linear segments. We show that quantum transport is enhanced by interconnecting more layers of dendrimers.

Relaxation dynamics of generalized scale-free polymer networks

We focus on treelike generalized scale-free polymer networks, whose geometries depend on a parameter, γ, that controls their connectivity and on two modularity parameters: the minimum allowed degree, Kmin, and the maximum allowed degree, Kmax. We monitor the influence of these parameters on the static and dynamic properties of the achieved generalized scale-free polymer networks. The relaxation dynamics is studied in the framework of generalized Gaussian structures model by employing the Rouse-type approach. The dynamical quantities on which we focus are the average monomer displacement under external forces and the mechanical relaxation moduli (storage and loss modulus), while for the static and structure properties of these networks we concentrate on the eigenvalue spectrum, diameter, and degree correlations. Depending on the values of network’s parameters we were able to switch between distinct hyperbranched structures: networks with more linearlike segments or with a predominant star or dendrimerlike topology. We have observed a stronger influence on Kmin than on Kmax. In the intermediate time (frequency) domain, all physical quantities obey power-laws for polymer networks with γ = 2.5 and Kmin = 2 and we prove additionally that for networks with γ ≥ 2.5 new regions with constant slope emerge by a proper choice of Kmin. Remarkably, we show that for certain values of the parameter set one may obtain self-similar networks.

Dynamics of a Polymer Network Modeled by a Fractal Cactus

In this paper, we focus on the relaxation dynamics of a polymer network modeled by a fractal cactus. We perform our study in the framework of the generalized Gaussian structure model using both Rouse and Zimm approaches. By performing real-space renormalization transformations, we determine analytically the whole eigenvalue spectrum of the connectivity matrix, thereby rendering possible the analysis of the Rouse-dynamics at very large generations of the structure. The evaluation of the structural and dynamical properties of the fractal network in the Rouse type-approach reveals that they obey scaling and the dynamics is governed by the value of spectral dimension. In the Zimm-type approach, the relaxation quantities show a strong dependence on the strength of the hydrodynamic interaction. For low and medium hydrodynamic interactions, the relaxation quantities do not obey power law behavior, while for slightly larger interactions they do. Under strong hydrodynamic interactions, the storage modulus does not follow power law behavior and the average displacement of the monomer is very low. Remarkably, the theoretical findings with respect to scaling in the intermediate domain of the relaxation quantities are well supported by experimental results from the literature.

Dynamics of a Complex Multilayer Polymer Network: Mechanical Relaxation and Energy Transfer

In this paper, we focus on the mechanical relaxation of a multilayer polymer network built by connecting identical layers that have, as underlying topologies, the dual Sierpinski gasket and the regular dendrimer. Additionally, we analyze the dynamics of dipolar energy transfer over a system of chromophores arranged in the form of a multilayer network. Both dynamical processes are studied in the framework of the generalized Gaussian structure (GSS) model. We develop a method whereby the whole eigenvalue spectrum of the connectivity matrix of the multilayer network can be determined iteratively, thereby rendering possible the analysis of the dynamics of networks consisting of a large number of layers. This fact allows us to study in detail the crossover from layer-like behavior to chain-like behavior. Remarkably, we highlight the existence of two bulk-like behaviors. The theoretical findings with respect to the decomposition of the intermediate domain of the relaxation quantities, as well as the chain-like behavior, are well supported by experimental results.